Transfer Functions (General Question)

[Burner]

Homework Statement

Just a generic question. If you have Laplace-transformed differential equation like s³Y + sY = g/s + X, where g is a constant, how do you handle manipulating the equation to get the transfer function Y/X? I feel like I've done this before, but I'm having a severe mental block.

2. The attempt at a solution

I've had some thoughts, but can't get anywhere with them. The constant g has nothing to do with X, so any attempts at factoring have been unsuccessful. I thought about some kind of superposition, but am not sure how that would work. Any guidance or hints would be greatly appreciated. Thanks!

 

[kentigens]

try move the g/s over to the left side of the equation. s3Y + sY - g*s-1 = X. Then do the transformation(use the table).

 

[Burner]

Thank you, but let me try to clarify a bit.

I don't require getting it back into the time domain. I'm just trying to find the transfer function with an output Y for an input X (in the s domain). To illustrate the problem I am encountering, simplifying you'll get Y(s⁴ + s²) = g + sX. The problem is that I need the quantity Y/X in terms of only g and s, and dividing both sides by X doesn't quite get the job done.

My thought is that there might be a partial fraction expansion or something I am missing.

 

[Burner]

Correct me if I'm wrong, but after a bit more reading and thinking: For the purposes of a useful transfer function, the constant term can be dropped because it is representative of an initial condition, right?